In 1929, astronomer Edwin Hubble
made an unusual discovery.
He noticed that most of the galaxies in the universe
are moving away from us, which led
him to realize that the universe is expanding,
and that expansion has strange implications.
It means that everything in the universe, even light,
gets stretched out.
So when light gets redshifted-- that is its wavelength
gets stretched out and it becomes a cooler color--
is energy conserved?
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Let's first look at how this red shift happens.
Imagine the expansion of the universe like a loaf of raisin
bread, rising as it bakes.
Galaxies, like the reasons in the loaf,
spread apart, not because they're
moving through the loaf, but because the dough, itself,
is expanding, just like spacetime does.
As spacetime gets stretched out, so
do any of the light waves that travel through it.
This is known as cosmological redshift.
Imagine a galaxy far away emits some yellow light at you.
We would measure that light as more stretched out,
so maybe we would see it as more red.
That's why we call this redshift, because the longest
wavelengths of visible light are in the red part
of the spectrum.
Note that this cosmological red shift
is different from Doppler redshift or blueshift, which
is caused by things moving toward or away
from us through space.
Now, longer wavelengths of light have less energy,
or at least Planck's equation tells us that.
Energy equals Planck's constant times the speed of light
over the wavelength, so as light's wavelength gets longer,
its energy decreases.
But wait.
You learn in intro physics about the law of conservation
of energy, that energy can neither be created
nor destroyed.
It's just transferred from one form into another.
So where does the redshifted photon's energy go?
One could guess that, well, maybe light waves die out
the same way a ripple in water dissipates,
but the water molecules are bumping into each other,
stealing kinetic energy through friction
away from the wave's energy until the ripple finally
dies out.
Total energy is conserved, though.
In contrast, light from a galaxy is not
traveling through a medium.
Most of space is near emptiness.
There is no air resistance or friction,
so there is nowhere to pass the energy.
So if the light wave isn't giving up energy,
then where is the energy going?
Well, the short answer is, actually, energy
isn't conserved.
The photon's energy is just lost.
Seems freaky, right?
I just told you that the law of conservation of energy
doesn't always hold, but there is
nothing to worry about if we think back to how we first
came up with this law.
Physicists first developed the law of conservation of energy
by doing experiments, like when they saw boiling steam lift
a pot lid, indicating that heat could be transformed
into mechanical energy.
And burning wax transforms chemical energy
in the molecular bonds into heat energy, and so on.
But in 1915, Emmy Noether proved a logical reason
for why energy is conserved.
Noether's theorem stated conservation laws
can be derived from symmetries in the universe.
For example, she proved using math
that energy conservation is a consequence of when you assume
that the laws of physics don't change
over time, what physicists call time invariance.
If you threw a ball in the air today,
time invariance says that it will rise and fall
exactly the same way tomorrow or a billion years from now,
but are the laws of physics actually unchanging in time?
In that same year that Noether published her theorem,
Einstein showed using general relativity
that spacetime can change.
It can warp and ripple and expand.
In fact, the first observed gravitational waves,
a couple weeks ago, are an example of spacetime changing.
If spacetime, itself, is changing,
then that means that the laws of physics must also be changing,
which means, by Noether's theorem,
energy isn't conserved anymore.
So during cosmological redshift, when a photon's wavelength
gets stretched out, its energy is simply lost.
So it turns out that something we usually
talk about as a universal truth has cosmological exceptions.
What do those exceptions mean?
For me, they are a reminder that everything
we know and intuitively understand
is far from universal.
It's a special case.
There is an old folk tale about a frog that
lived his entire life down a well,
and everything there made sense to him.
He knew where the bugs hid.
He knew where the comfortable rocks were, until one day
a turtle showed up and told him about the outside world, about
mountains and trees and oceans.
And the frog just couldn't wrap its head around it.
He couldn't imagine anything that
was bigger or better or different from his own well.
The law of conservation of energy
applies down our own well.
For almost everything we experience as humans
on a daily basis, sure, it's accurate enough
to say that the laws of physics don't change over time,
and so energy is conserved.
But when you zoom out, the physics starts to look foreign.
There is more to the story.
Thank you so much for watching, and happy physicsing.
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